从电生理信号重建相位-振幅动力学
Reconstruction of phase-amplitude dynamics from electrophysiological signals
AI总结：
提出一种从电生理信号直接重建相位-振幅动力学的新方法，利用Koopman算子特征函数和参数化方法估计脑区耦合，构建相位-振幅振荡器网络。
摘要：
我们提出了一种新方法，直接从测量的电生理信号中重建相位-振幅动力学，以估计大脑区域之间的耦合。为此，我们利用了振荡系统相位-振幅约化领域的最新进展，该进展允许使用与Koopman算子特征函数相关的变换（参数化）将非耦合振荡系统以唯一形式表示为相位-振幅振荡器。通过结合参数化方法和Fourier-Laplace平均方法来寻找Koopman算子的特征函数，我们开发了一种从相互作用的振荡系统信号中评估变换函数的方法。所得到的重建动力学系统是一个相位-振幅振荡器网络，它们之间的相互作用以相位和振幅坐标中的耦合函数表示。
英文摘要：
We present a novel method of reconstructing the phase-amplitude dynamics directly from measured electrophysiological signals to estimate the coupling between brain regions. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates.
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